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Three different methods for testing all pairs of yȳk, - yȳk’ were contrasted under varying sample size (n) and variance conditions. With unequal n’s of six and up, only the Behrens-Fisher statistic provided satisfactory control of both the familywise rate of Type I errors and Type I error rate on each contrast. Satisfactory control with unequal n’s of three and up is dubious even with this statistic.

Numerous studies have documented the robustness of t and F to heterogeneous variances under the restricted condition of equal n's. Likewise, the distortion of 01. in the presence of unequal n's and variances has been demonstrated in both mathematical and empirical studies. Several investigations, however, have shown the Welch technique to be robust to this disturbing situation in the two group case. The present study was addressed to the k group AOV situation. Monte Carlo methods were employed to contrast several procedures with respect to a.) control over Type I errors and b.) power. Results indicate that the generalized Welch technique may be substituted for the AOV when variances are heterogenEous and n's are unequal.A TEST OF THE null hypothesis, H 0 : fJ. 1 =fJ. 2 = ... (J.k is generally conducted through analysis of variance (AOV) procedures. With K independent samples, the derivation assumes that the population variances are equal. In practice, however, the condition of homogeneous variances cannot always bernet. The effect of heterogeneous variances on the probability of a Type I error has been the subject ofboth J:IRthematical and empirical studies. As the review below will demonstrate, the effect of heterogeneous variances is generally not serious when n's are equal and of reasonable size, but when n's are unequal protection against Type I errors rapidly deteriorates.

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